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Feb
11
revised Derivative of remainder function.
deleted 29 characters in body
Feb
11
awarded  Commentator
Feb
11
awarded  Scholar
Feb
11
accepted Derivative of remainder function.
Feb
11
comment Derivative of remainder function.
Better? Yeah! Surely. Accepted. Thank you for the constructive approach.
Feb
11
comment Derivative of remainder function.
Really, it is hard to mentally move from thoughts about integer constants to thoughts about the real-valued functions.
Feb
11
comment Derivative of remainder function.
Hmm... $[a / b]$ difenitely have steps when dividend growth and passes the points of multiplicity with respect to divisor. In such points the quotient have integer values.
Feb
11
comment Derivative of remainder function.
$a'(x)$ is an answer only when $a(x) < b(x)$
Feb
11
awarded  Supporter
Feb
11
comment Derivative of remainder function.
If $[\cdot]$ is constant regardless of constancy of an argument, than derivative is $a'(x) - [a(x)/b(x)] \cdot b'(x)$ except the points, where $a(x) = n \cdot b(x)$ for some natural $n$. Isn't it?
Feb
11
comment Derivative of remainder function.
@AndréNicolas Interesting note. I'll try to find the solution for polinomials.
Feb
11
awarded  Student
Feb
11
comment Derivative of remainder function.
@MPW I think there are at least two cases: when lhs < rhs and vice-versa.
Feb
11
awarded  Editor
Feb
11
revised Derivative of remainder function.
added 193 characters in body
Feb
11
comment Derivative of remainder function.
@AndréNicolas It's incredible. I intuitively feel that the solution is expressed in terms of elementary functions or even of couple of multiplications, additions, subtractions and divisions of operands and its first derivatives.
Feb
11
asked Derivative of remainder function.